Solve the following integration corrected to 3 decimal places using: 1. Trapezoidal rule 4 intervals 2. Simpson's rule 4 intervals, Compare the Results -5 4 dx x

Q: Function h is graphed. h -4 -3 -2 L y 4 3+ 2- 1 -1- -2+ -3- 12 3 4 Find h(2) da. Give an exact…

A: This question can be solved using the concept of area under curve.

Q: Q1llenn Prove the following using the principle of mathematical induction. For n ≥ 1, 1 1 1 1 3/2 +…

A: Given; 1/52+1/54+...+1/52n=(1-1/25n)1/24.

Q: t = b? Choose 1 answer: b Ⓒ / ° v A a © B Ⓒ a b cb a a b e20t+t6 dt e10t+t³ dt 10e10t+ 3t² dt…

A: Topic = Integration

Q: Consider the parametric curve: x = sin² (t) y = -9t Which integral gives the arc length of the curve…

A:

Q: 2. A particle is moving in space with position function (t) = (sin(3t), cos(3t), 3 – 4t). 2.1. Find…

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Q: (2) Z/(5) =....... (i) (5) (ii) 5Z (iii) {[0],[1],[2],[3],[4]}

A: We have to find the operation

Q: 6. I. Evaluate each determinant. тут 3-3 4 1 0-1 -1 -4

A: Given data

Q: Determine the magnitude of the vector difference V-V₂-V₁ and the angle 8, which V' makes with the…

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Q: 9. Find the volume of the solid obtained by rotating the region R enclosed by y = -x² + 6x-8 and y =…

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Q: 5. Use Cartesian coordinates to evaluate ƒƒƒ v³² av where D is the tetrahedron in the first octant…

A: Given problem:-

Q: 4 Find the general Solution of the following PDES • з Их + 2 Иу -Х ucx, c) - че 2 (зу-2х)12 ans3-…

A: To find the general solution of the given PDE .

Q: show that V(x, y) = x 'f (2x+y) is the general Solution of av X du 2X 1 = V ду dax

A: Explanation of the answer is as follows

Q: 7. Compute the area of the region R enclosed by the curves y = x² - 1 and y = 1- x.

A: We have to find out the area

Q: Find the solution of the given initial value problem in explicit form. ㅠ sin (2x) dx + cos(9y) dy =…

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Q: (3) If R is an integral domain has non zero characteristic, then Char(R)=..... (i) 5 (ii) 4 (iii)9

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Q: Short Answer 11. Calculate X+W for X- 3) 2 and W- or explain why this operation

A: Given X=70-1423 and W=-4111-122To Find:  X+W

Q: I. 7. Evaluate each determinant. -3 4 -5 2 -5 1 5 3

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Q: A and b

A: We need to solve maxima/minima problem.

Q: For each of the following ,find fx fy fxx fy fyx and fxy f(x, y) = x cos+ ye*. 2.f(x,y) = y²x¹e². 3.…

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Q: y"" - 4y" + 3y = 0

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Q: dx (x² +25)3/2

A: To find the integration.

Q: 1. Find the Inverse Laplace Transforms of the following. 4) 48-60√s s4

A: A detailed solution is given below.

Q: 1. Find the angle between two vectors a and b with magnitudes √3 and 2, respectively having a b =…

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Q: 2. Evaluate the double integral that will find the volume of a solid bounded by 21-2y²-322 and the…

A: Given: z=1-2y^2-3x^2 and xy-plane

Q: (1) Let I be a proper ideal of the commutative ring R with identity. Then I is a ........ if and…

A: (1) we have to fill in the blanks Let I be a proper ideal of the commutative ring r with identity.…

Q: Set up but do not evaluate an integral that represents the volume of the solid of revolution…

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Q: 1. Find S [*¹ f(x) dx given ² f(x) dx = 2 and ¹ √ ² f(x) dx = 3

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Q: (x² - y²)²] 1²₁ 1² du du dt x+y Evaluate: ₁ S

A: Given ∫-13∫02x2-y22x+ydudt Since x2-y22x+y is constant with respective u and t, we take constant out…

Q: Suppose f(x) = 6t²√1+t³ dt. 1) Evaluate f (2). 2) Evaluate f'(2). 3) Evaluate f"(2).

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Q: 4. Evaluate the double integral: Y SZ (Hint: Change the order of integration to dy dx.) dx dy. +1…

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Q: Write down a differential equation of the form = ay + b whose ay dt all other solutions diverge from…

A: Here, the differential equation is of the form  dydt=ay+b⇒dydt=ay+ba⇒dyy+ba=a dt⇒∫dyy+ba=∫a…

Q: Let a, b ∈ R. a) Find the determinant of  a 2  b -2 1 2 4 -2 -1   b) Suppose u, v, and w are…

A: Concept: Determinant of the matrix: The determinant of the matrix is the expansion of the matrix…

Q: a A person's intelligence quotient (IQ) is measured by the function I(m, a) = 100m where a is the…

A: see below the answer and explanation

Q: Q4: A) For each of the following ,find fx fy fex fyy fyx and fxy 2.f(x, y) = sin²(x-3y) 3.f(x,y) =…

A: Solution: The objective is to find the partial derivatives of the given functions

Q: Given g(x) = -10x-2 -5x-2' Provide your answer below: g'(x) = find g'(x) using the definition of a…

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Q: (1) Let I be a proper ideal of the commutative ring R with identity. Then I is a ........ if and…

A: 1) Let I be a proper ideal of commutative ring R with identity. Then I is a ............. if and…

Q: Find the solution of the given initial value problem in explicit form. 7x y' = , y(0) = -9 y + x²y…

A: In this question, we will solve the given IVP.

Q: show that V(x,y) = x 'f (2x+y) is the general Solution of : x av dx 2x du 1 = V ay

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Q: The value of A. +3+2x² +C C. = + x² +2+C 20 [ (² + 3) *²x² dx B. +³²+3x³ + C 28 D. none of the…

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Q: I. Solve the following integrals completely and honestly. Show your solution in ink and as neatly as…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Find the area of the region enclosed by the curves y = x³ and y = 4x. 24 8 16

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Q: 2 3) 9 = x ² sin x y વચ્ચે ઝ 4) y = sin x 1-2 cos x

A:

Q: 12. A thin 4 cm wire represented by 1 < x < 5 has density function p(x)=19/cm. Find the mass of the…

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Q: Let F(x,y)=ln(x² + y²), then answer the following (4) Find the boundary of the function's domain.…

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Q: 1. Solve the following Linear Systems of Equations by Gaussian Elimination: 2.) 3x + 3z = 0 2x +2y =…

A: On solving this we will get

Q: Find S dx √X²-2x+1

A: ∫1x2-2x+1dx=∫1x-1dx=lnx-1Add a constant to the solution=lnx-1+C

Q: Solve the boundry-Valued PDE 24 = 4 24 = 484 ठेप ulo,д) =8 ёру using the genval method -12X-39 ans:…

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Q: Write out the first four terms of the Maclaurin series of f(x) if f(0) = -9, f'(0) = -9, f(x) = +...…

A: Topic = Series

Q: 1. The simple interest charged on a 60-day loan of Php 8,400.00 is Php 119. Find the simple interest…

A: Use simple interest formula

Q: an+1 Suppose that an ∞ Σ απ( – 81)" man n=1 →1 as n→ ∞o. Find the radius of convergence.

A: Explanation of the answer is as follows